Erin Bennett, Judith Degen, Michael Henry Tessler, Justine Kao & Noah D. Goodman (Stanford)
relevance
Â
problem
  Â
INSERT A COOL PICTURE??
sentence
Joe eats many burgers.
Â
cardinal surprise reading
Joe eats more burgers that we would expect of him.
  Â
INSERT A COOL PICTURE
(e.g., Schoeller & Franke 2015)
real-world frequencies
Â
experimental measures
take average normalized slider ratings to reflect population-level belief
goal: scrutinize BH task
dummy
approach: hieararchical Bayesian modeling
dummy
dummy
dummy
general
Â
specific
red: averaged normal. slider ratings; black: mean posterior \(Q_i\) with 95% HDIs
black: mean posterior \(Q_j\) with 95% HDIs; dark gray: mean posterior \(P_{ij}\)
Â
avrgd normlzd slider ratings we would expect from the model and the posterior distribution over parameters is virtually indistinguishable from the observed
some frequencies of number choices are suprising for the trained model (but: little data to go with; round or salient numbers may play a role)
miserable failure to predict why it should be more likely that no marble sank than that one marble sank (alternative explanation: subjects revise beliefs, assume homogeneous "wonkiness" of marbles)
dummy
dummy
dummy
dummy
dummy
w = 20
w = 200
dummy
kappa = 1.2, sigma = 0.5
kappa = 2, sigma = 1.5
dummy
qplot(sample(x = 5, size = 1000, replace = TRUE, prob = exp(a *(1:5))))
a = 0.5
a = 1.5
\[p^\text{high}_{ijl} = \begin{cases} 2 & \text{if $mode(P_{ij})$ is closer to higher} \\ & \text{ bin of $l$ than to lower bin } \\ 1 & \text{if equal distance} \\ 0 & \text{otherwise} \end{cases}\]
\[p^\text{low}_{ijl} = 2 - p^\text{high}_{ijk}\]
example